I don't know enough about the biology behind them to make some big case against them and the specific reasons
why they are illegal. I know the generalities and physical problems from roid use, but I'll defer to someone better informed than me on that subject.
But, the fact is, they are illegal and they do grant an unfair advantage to those who choose to break the rule over those who don't. The cortisone analogy is compelling but it's just not quite there for me... there's a world of difference between correcting an injury and taking something to allow you to recover at a superhuman rate versus your competitors.
I think that by and large, we still value integrity and honesty in sport (one of the few places we still do), and to many, myself included, the integrity of allowing the combination of hard work and natural ability (i.e., not enhanced by drugs) to better oneself is an attractive part of sports. Yes, there are biological deficiencies and advantages among competitors.
I'm 5'8", I had to play tennis in college instead of basketball, the other sport I love... Even in tennis, the trend is moving towards taller players (a 6'7 guy just won the US Open... you hardly see anyone under 6' out there having success today). I had some marked disadvantages over the taller guys I played... but some big advantages too (bend knees easier, mobility, agility). That's what makes sports fun... being able to pick apart your opponent and his weaknesses, using your strengths to your advantage.
Yes, some guys have ridiculous biological traits (Phelps' body for swimming comes to mind... and yes, Manny's NATURAL hitting ability) and that's luck of the draw. That's something to be marveled at. That's why we watch pro sports - to live vicariously through these superhuman athletes. They are incredibly gifted and we want to see something better and bigger than anything we could ever achieve for ourselves in these players. Part of that rush comes from knowing that these guys are just simply natural physical specimens who have honed their abilities through hard work and natural means. Find out these guys are taking drugs to get there and all of a sudden maybe they aren't so impressive. The other side of that is that it's disappointing to see someone who indeed has SO MUCH natural ability like Manny, one of the best hitters of all time, to be implicated. He didn't need that shit!
Knowing that these guys used artificial means to get there takes away the thrill factor of it - and there's no question about many of the cases, like your own Big Papi. He's a joke! It'd be one thing if the steroids didn't have a noticeable impact, but when the whole way a sport is played on account of illegal doping, it robs the sport of its essence.
Edit: Admittedly, the line gets blurred when you start putting vitamin supplements, protein shakes, and all that kind of stuff into the equation, especially when the legends of yesteryear didn't have access to this kinda stuff. But, if David Ortiz can be the player he once was popping a Centrum Gold and some Magnesium and a Whey Shake once a day, more power to him...
Edit 2: And I guess that above point kinda sums up the whole cortisone analogy and why it doesn't work for me. It's not going to enable someone to perform past their abilities. And I'm just using Manny and Ortiz as examples because (1) I know you know about them and (2) They both knocked my 07 Tribe out of a near-sure WS win

. I know there are plenty of players out there to serve as perfect case studies.